The Time Of Arrival (TOA) of radio signals is used by many applications running on wireless networks for synchronizing the network clocks, for measuring the distance between two terminals or for computing positions. The accuracy of position services (i.e. Geographic, Geocentric or Relative positioning) depends on the accuracy of the measurement of Time Of Arrival. From TOA can be deducted the Time Of Flight (TOF), the Time Difference Of Arrival (TDOA), the clock shift and other time related entities that can be used in specific algorithms for computing the position of an object in relation with others or for synchronizing clocks.
Radio signals travel from the transmitter to receiver on one direct path and on several indirect paths. Indirect paths are caused by reflections, refractions and scattering (diffusion) of radio signals. Reflections are caused by radio waves bouncing on flat surfaces like vertical walls, horizontal concrete or asphalt covered surfaces, horizontal body of water, etc. Refractions are changes of the direction of propagation path when the signal travels through anisotropic media. Variations in air temperature, humidity and density cause the phenomenon known as the atmospheric refraction that makes the electromagnetic radiation to follow a curve path. For some terrestrial applications when the relative distances between the transmitter and receiver are small, the effect of reflection of the direct path is smaller that it can be measured therefore it can be ignored. Scattering of radio signals happens when signals travel through objects smaller than the wavelength of the electromagnetic signal, like edges of metallic furniture, edges of buildings, top of mountains, etc.
Indirect signals arrive at receiver later than the direct signal, because their paths are longer than the direct path.
TOA of radio signals can be measured by transmitting an analog impulse or by transmitting a numerical sequence of pseudo-random bits that are used for computing the impulse response.
The analog method of transmitting one radio impulse has the advantage of providing a very clear “view” of the direct and reflected signals, allowing the identification of the time of arrival of each of them with a precision as good as the length of the impulse. The disadvantage of the method consists on the fact that the duration of the impulse is too short to have enough energy for propagating very far. In order to propagate the impulse at practical distances, it is necessary to use very high transmit power. Because the impulse duration is very short, the energy spectrum of the impulse signal is very large, interfering with communications over a large frequency spectrum. This fact restricts the use of analog impulses for measuring practical distances.
The digital method of impulse-response consists in transmitting a sequence of pseudo-random bits (pn). Gold codes are the most used pn sequence because they offer a good autocorrelation. As they arrive at receiver, the bits of the pn sequence are stored in a shifting a register that is cross-correlated with the same pn sequence as the one used at transmitter. When all, or almost all received bits match the witness pn sequence, the cross-correlation function has a significant peak and the TOA is computed as the difference between the content of the clock register at that moment and the time needed for transmitting the pn sequence. The method requires very small energy for transmitting the signal at very large distances and offers precision as good as the clock tick. Mathematical methods for computing the TOA with higher precision than one clock tick are presented, for example, in United States patent application number 20030227895 to Strutt et al. entitled “System and method for improving the accuracy of time of arrival measurements in a wireless ad-hoc communications network” and U.S. Pat. No. 6,269,075 to Tran entitled “Finger assignment in a CDMA rake receiver”, both of which contents are incorporated by reference herein.
The disadvantage of the method using the pn sequence consists in the difficulty of separating between the TOA of the direct path and the TOA of reflected paths, when the length of the reflected paths is very close to the length of the direct path. Because the clocks of transmitter and receiver do not tick in the same time, each bit of the pn sequence has to be transmitted for at least two clock ticks, or the receiver should sample the signal twice as fast as it is transmitted. It makes sure that a complete received bit matches one bit of the pn witness sequence, not only a fraction of it. At a 32 MHz (Megahertz) clock frequency, each bit is transmitted during two clock ticks, or 62.5 ns (nanoseconds). Therefore, if the direct and one reflected path have a difference of length smaller than 20 m (meters), they cannot be easily identified with the impulse-response method because the time passed between receiving the direct signal and receiving the indirect signal is less than 60 ns. The problem becomes even more difficult, if a large number of reflected signals arrive over a long period (hundreds of ns) of time, but at close interval one to another. Such response is characteristic to reflections on very rough surfaces.
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